The following is a linear programming model for analyzing the product mix of Maxine$$s Hat Company, which produces three hat styles:

The POM for Windows printout below shows the optimal solution to the problem. Consider each of the following statements independently and state whether it is true or false. Explain each answer but do NOT resolve the problem but use the analysis above to answer the questions.

$1.$ If the price of hat $3$ were increased to $$10\mathrm{.}50,$ it would be part of the optimal product mix. Hint: Hat $3$ is represented by X$3$ and its optimal value currently is $0,$ which means that it is not to be produced and not part of the optimal product mix.by being part of the optimal product mix, this means having a non$-$ zero value in the optimal solution